Chang’s Conjecture with $$\square _{\omega _1, 2}$$ from an $$\omega _1$$-Erdős cardinal
Abstract Answering a question of Sakai (Arch Math Logic 52(1–2):29–45, 2013), we show that the existence of an $$\omega _1$$-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with $$\square _{\omega _1, 2}$$. By a result of Donder (In: Set theory and model theory (Bonn, 1979),...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Neeman, Itay [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Archive for mathematical logic - Springer Berlin Heidelberg, 1988, 59(2020), 7-8 vom: 21. Feb., Seite 893-904 |
|---|---|
| Übergeordnetes Werk: |
volume:59 ; year:2020 ; number:7-8 ; day:21 ; month:02 ; pages:893-904 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00153-020-00723-w |
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OLC2119848114 |
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10.1007/s00153-020-00723-w doi (DE-627)OLC2119848114 (DE-He213)s00153-020-00723-w-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Neeman, Itay verfasserin aut Chang’s Conjecture with $$\square _{\omega _1, 2}$$ from an $$\omega _1$$-Erdős cardinal 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract Answering a question of Sakai (Arch Math Logic 52(1–2):29–45, 2013), we show that the existence of an $$\omega _1$$-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with $$\square _{\omega _1, 2}$$. By a result of Donder (In: Set theory and model theory (Bonn, 1979), volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of $$\square _{\lambda , 2}$$ and $$(\lambda ^+, \lambda ) \twoheadrightarrow (\kappa ^+, \kappa )$$ for uncountable $$\kappa $$. Chang’s Conjecture Square Erdos cardinal Forcing Susice, John aut Enthalten in Archive for mathematical logic Springer Berlin Heidelberg, 1988 59(2020), 7-8 vom: 21. Feb., Seite 893-904 (DE-627)130412910 (DE-600)623073-8 (DE-576)015915948 0933-5846 nnns volume:59 year:2020 number:7-8 day:21 month:02 pages:893-904 https://doi.org/10.1007/s00153-020-00723-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 GBV_ILN_4277 AR 59 2020 7-8 21 02 893-904 |
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Abstract Answering a question of Sakai (Arch Math Logic 52(1–2):29–45, 2013), we show that the existence of an $$\omega _1$$-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with $$\square _{\omega _1, 2}$$. By a result of Donder (In: Set theory and model theory (Bonn, 1979), volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of $$\square _{\lambda , 2}$$ and $$(\lambda ^+, \lambda ) \twoheadrightarrow (\kappa ^+, \kappa )$$ for uncountable $$\kappa $$. © Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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Abstract Answering a question of Sakai (Arch Math Logic 52(1–2):29–45, 2013), we show that the existence of an $$\omega _1$$-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with $$\square _{\omega _1, 2}$$. By a result of Donder (In: Set theory and model theory (Bonn, 1979), volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of $$\square _{\lambda , 2}$$ and $$(\lambda ^+, \lambda ) \twoheadrightarrow (\kappa ^+, \kappa )$$ for uncountable $$\kappa $$. © Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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Abstract Answering a question of Sakai (Arch Math Logic 52(1–2):29–45, 2013), we show that the existence of an $$\omega _1$$-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with $$\square _{\omega _1, 2}$$. By a result of Donder (In: Set theory and model theory (Bonn, 1979), volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of $$\square _{\lambda , 2}$$ and $$(\lambda ^+, \lambda ) \twoheadrightarrow (\kappa ^+, \kappa )$$ for uncountable $$\kappa $$. © Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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2024-07-04T02:28:14.965Z |
| _version_ |
1803613734140116992 |
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By a result of Donder (In: Set theory and model theory (Bonn, 1979), volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. 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